CSDI: Conditional Score-based Diffusion Models for Probabilistic Time\n Series Imputation

Abstract

The imputation of missing values in time series has many applications in\nhealthcare and finance. While autoregressive models are natural candidates for\ntime series imputation, score-based diffusion models have recently outperformed\nexisting counterparts including autoregressive models in many tasks such as\nimage generation and audio synthesis, and would be promising for time series\nimputation. In this paper, we propose Conditional Score-based Diffusion models\nfor Imputation (CSDI), a novel time series imputation method that utilizes\nscore-based diffusion models conditioned on observed data. Unlike existing\nscore-based approaches, the conditional diffusion model is explicitly trained\nfor imputation and can exploit correlations between observed values. On\nhealthcare and environmental data, CSDI improves by 40-65% over existing\nprobabilistic imputation methods on popular performance metrics. In addition,\ndeterministic imputation by CSDI reduces the error by 5-20% compared to the\nstate-of-the-art deterministic imputation methods. Furthermore, CSDI can also\nbe applied to time series interpolation and probabilistic forecasting, and is\ncompetitive with existing baselines. The code is available at\nhttps://github.com/ermongroup/CSDI.\n